Cooperative binding systems are being studied taking into account site or submit interactions, ligand interactions, aggregation and redistribution in proteins and model systems. Methods are being developed to evaluate reasonable parameters describing these reactions. While we study amino acids where the number of sites is small, our emphasis has been on those systems such as protein-DNA interactions and the hellix-coil transition where the number of sites is large. The usual method of analysis for these systems has involved approximations assuming an infinite number of sites. We, on the other hand, have developed an exact combinatorial approach to this problem. Our formalism analyzes both small and large numbers of sites and requires only reasonable times on the present high-speed computers. Generation of the exact polynomials describing these systems has permitted us to examine in detail properties of the reactions which were previously unknown. Our emphasis at present is on the analysis of the relationship between nearest neighbor interactions and the temperature under which a given reaction occurs.